Explanation:
To find the equation of the line passing through the points (3, -6) and (-5, 4), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
First, let's calculate the slope (m) using the given points:
m = (y2 - y1) / (x2 - x1)
m = (4 - (-6)) / (-5 - 3)
m = 10 / (-8)
m = -5 / 4
Now, let's choose one of the points, let's say (3, -6), and substitute the values into the point-slope formula:
y - y1 = m(x - x1)
y - (-6) = (-5/4)(x - 3)
y + 6 = (-5/4)(x - 3)
Now, we can simplify and rearrange the equation into slope-intercept form (y = mx + b):
y + 6 = (-5/4)x + (15/4)
y = (-5/4)x + (15/4) - (24/4)
y = (-5/4)x - 9/4
So, the equation of the line passing through the points (3, -6) and (-5, 4) is:
y = (-5/4)x - 9/4